# ATMS 305, Fall 2024 -- Lab20: Correlation
# Today we'll start talking about statistics with: Correlation
#
# Info:
#  scipy stats tutorial: https://docs.scipy.org/doc/scipy/tutorial/stats.html
#  scipy lectures/stats: https://scipy-lectures.org/packages/statistics/index.html
#  Pearson correlation coefficient: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
#

# >> A. IMPORT
#
#  1. import as usual: (a) numpy (b) matplotlib.pyplot (c) pandas
#  2. add to this:
#        import scipy as sp
#        import plotly.express as px
#        from scipy.signal import find_peaks
import scipy as sp
import plotly.express as px
from scipy.signal import find_peaks
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# >> B. CORRELATION COEFFICIENT (Markdown figure)
#
#  We're going to generate some curves and compute their correlation -
#    .. in particular, their *correlation coefficient*.
#
#  Wikipedia has a nice figure for this.
#  a) Insert a text cell below this one. We'll use Markdown next.
#  a) Show a heading "CORRELATION" first --
#       ... help:  https://python-markdown.github.io/extensions/toc/
#  b) After the above heading, display the image listed below
#       ... help:  https://stackoverflow.com/questions/10628262/inserting-image-into-ipython-notebook-markdown
#       ... >URL:  https://upload.wikimedia.org/wikipedia/commons/3/34/Correlation_coefficient.png

# >> C. SINE CURVES
#
# Now you generate Two sine curves.
# These curves have a phase angle (shift) of 180 degrees: Opposites.
# This is the definition of "negative correlation."
#
# PLOTS:
#   1. After the y1= and y2= statements below, add plt.plot() code --
#      a) plot y1 as solid blue and
#      b) plot y2 as dashed red .. on the same plot figure!
#
#   2. Run the code.  Change nx to 20.  Run it again.
#      Much better!  That's all for this cell.
#
#   3. p.s.: NX is the number of "grid points" defining the curves;
#            angle is the phase shift angle (degrees) between y1, y2.
nx = 20
angle = 180.0
x = np.linspace(0., 2.*np.pi, nx)
y1 = 10 + 5*np.sin(x)
y2 = 20 + 5*np.sin(x - np.pi/180.*angle)

plt.plot(x, y1, 'b', label='y1')
plt.plot(x, y2, 'r--', label='y2')
plt.legend()
plt.grid()

# >> D. CURVES + CORRELATION
#
# STATS:
#   1. Let's use scipy.stat's "pearsonr()" routine to analyze the two
#      curves y1,y2.  pearsonr() returns two values.  Code it like this:
#
#            r,p = sp.stats.pearsonr(y1,y2)
#
#      r, the correlation coefficient, is the >>strength<< of the correlation.
#          r ranges from -1 to +1 like the figure you displayed earlier.
#          r=1 is "perfect" correlation.
#      p, or the 'p-value', is the >>probability<< we would find this result
#          from uncorrelated datasets. If p < 0.05 (5%), we say
#          the correlation "r" is **Statistically significant**
#
# PLOTS:
#   2. Repeat your plt.plot() statements from the last cell - here.
#      a) add label= statements to each plt.plot: "y1" and "y2"
#      b) add the legend.
#
#   3. Add xlabel: Array index  ..and.. ylabel: y1,y2 value
#   4. Add a title. Put the phase shift "angle", r, and p in the plot title.
#      >Do it like this (w/LaTeX formatting for degrees symbol, $^\circ$):
#
#        plt.title('%d$^\circ$phase, corr %.2f, p=%.2f' % (angle,r,p) );
#
# PEAKS:
#   5. Because we need it later, try scipy.signal's find_peaks() to show
#      where the y1 max is located ... then draw a dotted line at the peak.
#      As you will see, it is "close".  Add this code:
#
#           peaks,_ = find_peaks(y1);
#           plt.axvline(peaks,linestyle=':');    # vert line at peaks
#
#      FYI, the ",_" says to ignore other data returned by find_peaks().
r, p = sp.stats.pearsonr(y1, y2)
plt.plot(x, y1, 'b', label='y1')
plt.plot(x, y2, 'r--', label='y2')
plt.xlabel('Array index')
plt.ylabel('y1, y2 value')
plt.title('%d$^\circ$phase, corr %.2f, p=%.2f' % (angle,r,p) )

peaks,_ = find_peaks(y1)
plt.axvline(peaks,linestyle=':');    # vert line at peaks
plt.legend()
plt.grid()

<>:41: SyntaxWarning: invalid escape sequence '\c'
<>:41: SyntaxWarning: invalid escape sequence '\c'
C:\Users\theox\AppData\Local\Temp\ipykernel_14132\2318220278.py:41: SyntaxWarning: invalid escape sequence '\c'
  plt.title('%d$^\circ$phase, corr %.2f, p=%.2f' % (angle,r,p) )

# >> E. CORRELATION FOR A RANGE OF PHASE ANGLES
#
#  180 degrees was "out of phase" and gave a correlation of -1.
#  Here we try phase angles of 0, 90, ..., 360 degrees.
#
#  1. Start a figure with size 6,9 (or choose your own)
#  2. Start a for-loop whose loop variable "n" runs from 0-4 inclusive.
#     Inclusive: don't leave off "4" !!
#     This means you will make 5 plots in total.
#  3. INSIDE the loop:
#    a) plt.subplot(3,2,n+1)
#    b) set "angle" equal to n*90
#    c) use the same expression as previously:  y2 = ...
#    d) plot y1 and y2 as before with legend.
#    e) compute the pearson variables r,p as before.
#    f) use the same title as before.
#    g) don't worry about find_peaks() here.
#  4. Outside of the loop, call tight_layout
#
# CHECK: you should have 5 plots, "mostly" filling up a 3-row 2-column figure.
fig = plt.figure(figsize=(6, 9))

for n in range(0, 5):
    plt.subplot(3, 2, n+1)
    angle = n*90
    x = np.linspace(0., 2.*np.pi, nx)
    y1 = 10 + 5*np.sin(x)
    y2 = 20 + 5*np.sin(x - np.pi/180.*angle)

    r, p = sp.stats.pearsonr(y1, y2)
    plt.plot(x, y1, 'b', label='y1')
    plt.plot(x, y2, 'r--', label='y2')
    plt.xlabel('Array index')
    plt.ylabel('y1, y2 value')
    plt.title('%d$^\circ$phase, corr %.2f, p=%.2f' % (angle,r,p))
    plt.legend()
    plt.grid()
plt.tight_layout()

<>:35: SyntaxWarning: invalid escape sequence '\c'
<>:35: SyntaxWarning: invalid escape sequence '\c'
C:\Users\theox\AppData\Local\Temp\ipykernel_14132\2403100268.py:35: SyntaxWarning: invalid escape sequence '\c'
  plt.title('%d$^\circ$phase, corr %.2f, p=%.2f' % (angle,r,p))

# >> F. GET STORM SIMULATION DATA
#
# Now we'll shift to "real" data - well, a simulation of a supercell thunderstorm.
# This data follows a mesocyclone (storm rotation center) as it
#   intensifies and weakens, and the wind/rain/etc. near or above it.
#
# The first column is time, starting at 133 minutes.
#
#  1. Get this file:  rfd.atmos.uiuc.edu/305/supercell.txt
#
#  2. Use "!head -5 filename"      ...to see the first 5 lines of the file.
#     > There are two comment lines, then the headings line and data following.
!wget -q -N rfd.atmos.uiuc.edu/305/supercell.txt
import subprocess

subprocess.run(['wget', '-q', '-N', 'http://rfd.atmos.uiuc.edu/305/supercell.txt'])

with open('supercell.txt', 'r') as file:
    for _ in range(5):
        print(file.readline().strip())

Supercell storm simulation, Brian Jewett, Univ. Illinois Atmospheric Sciences

Time   dBZ2k dBZmx  RHsfc   Rain    P    VortSfc  VortAll VrtDepth   Usfc   Vsfc   Wlow    Wmin    Wmax   Tsfc    TPsfc  Tgrad   Qgr    Qra     Convg
133.00 -28.88 56.42  72.46   0.55   3.98  2339.78  3234.00  7740.93  -1.27  -3.00   0.503  -9.556  42.377 18.735  -5.082  6.301  0.000  0.099   -44.75
134.00  -0.85 59.45  67.94   2.70   3.54  3297.29  3818.93  9630.71   4.57 -20.40   0.737 -14.435  36.518 19.294  -4.523  2.399  0.000  0.061   -66.85

# >> G. READ STORM DATA
#
#  1. Read the data file with pandas' read_table() function into variable 'data'.
#     Use option skiprows= to skip over 2 comment lines mentioned previously.
#     You will also need this option: delim_whitespace=True
#
#  2. Finish with data.head(2) to make sure all is well.
#
#  3. FYI, we can refer to the 5th column with any of these:
#        data.Rain
#        data['Rain']
#        data.iloc[:,4]      # all rows, python column=4
#
#  4. FYI #2, data.shape reveals 48 rows (times) and 20 columns (fields).

data = pd.read_table('supercell.txt', skiprows=2, delim_whitespace=True)
data.head()

C:\Users\theox\AppData\Local\Temp\ipykernel_14132\4285391210.py:16: FutureWarning: The 'delim_whitespace' keyword in pd.read_table is deprecated and will be removed in a future version. Use ``sep='\s+'`` instead
  data = pd.read_table('supercell.txt', skiprows=2, delim_whitespace=True)

# >> H. QUICK SUMMARY
#
#  1. Use .describe() with your data array to get the min, max etc.
#
#  2. You should see min and max Time of 133 and 180, and maximum air
#     rotation (vorticity) at the ground (VortSfc) of 8928.9, which
#     is really 0.089 sec^-2. (stormy people: mesocyclone usually ~ 0.01/s^2)
data.describe()

# >> I. FIND AND LABEL PEAKS (in VortSfc, the surface rotation)
#
#  1. Use the find_peaks() function to identify the maxima in VortSfc.
#   a) call find_peaks as done before, but for array: data.VortSfc
#   b) results from find_peaks should be stored in "peaks" as before
#   b) add these options when calling find_peaks() to isolate the maxima:
#          distance=10
#          height=3000
#   c) we'll use the peak data in a moment.
#
#  2. plt.plot() field data.VortSfc versus data.Time
#    a) add xlabel: Time (min)
#    b) add ylabel: VortSfc x10^-5/s^2
#    c) add  title: Surface vorticity vs. time
#    d) use any color, or let plt.plot() pick for you
#
#  3. Plot an asterisk at each peak with:
#        plt.plot(data.Time[peaks],data.VortSfc[peaks],'*');
#
#  4. Draw a vertical dotted line at each peak with:
#       for xc in peaks:
#         plt.axvline(x=data.Time[xc],linestyle=':',color='tan');
peaks,_ = find_peaks(data.VortSfc, distance=10, height=3000)

plt.plot(data.Time, data.VortSfc)
plt.xlabel('Time (min)')
plt.ylabel('VortSfc x10^-5/s^2')
plt.title('Surface vorticity vs. time')
plt.plot(data.Time[peaks],data.VortSfc[peaks],'*')
for xc in peaks:
    plt.axvline(x=data.Time[xc],linestyle=':',color='tan')

# >> J. 3-PANEL PLOT
#
#  1. Do find_peaks again on data.VortSfc but use option: height=6000
#  2. Start a 12x6" figure, with a 1-row, 3-column plot.
#  3. On all 3 plots, use data.Time as the x-axis variable when plotting.
#  4. On all 3 plots, use xlabel: Time (min)
#
#  5. On left, plot Vortsfc (red) vs. time,
#              ylabel: VortSfc (x10^-5/sec),
#              title: Surface vertical vorticity
#  6. In middle, plot P (blue) vs. time,
#              ylabel: Pres (mb),
#              title: Surface perturbation pressure
#  7. On right, plot Wlow (green) vs. time,
#              ylabel: Wlow (m/s),
#              title: Low-level vertical motion
#
#  8. Now add code to plot vertical dotted lines at peak locations
#     for all 3 plot panels.  So after each subplot, x/ylabel
#     and title, you will repeat the "for xc in peaks..." code
#     used in the last cell.  You pick the line color.
#
#  9. Finish with tight_layout
#
# CHECK: when the storm's rotation intensifies (red curve), the
#   pressure falls, and a downdraft is produced soon after.
#   When we check, VortSfc and Pres will have negative correlation!

fig = plt.figure(figsize=(12, 6))
peaks,_ = find_peaks(data.VortSfc, distance=10, height=6000)

plt.subplot(1, 3, 1)
plt.plot(data.Time, data.VortSfc, 'r')
plt.xlabel('Time (min)')
plt.ylabel('VortSfc (x10^-5/sec)')
plt.title('Surface vertical vorticity')
for xc in peaks:
    plt.axvline(x=data.Time[xc],linestyle=':',color='tan')

plt.subplot(1, 3, 2)
plt.plot(data.Time, data.P, 'b')
plt.xlabel('Time (min)')
plt.ylabel('Pres (mb)')
plt.title('Surface perturbation pressure')
for xc in peaks:
    plt.axvline(x=data.Time[xc],linestyle=':',color='tan')

plt.subplot(1, 3, 3)
plt.plot(data.Time, data.Wlow, 'r')
plt.xlabel('Time (min)')
plt.ylabel('Wlow (m/s),')
plt.title('Low-level vertical motion')
for xc in peaks:
    plt.axvline(x=data.Time[xc],linestyle=':',color='tan')

plt.tight_layout()

# >> K. OVERLAY 2-AXIS PLOT (of VortSfc and Pres vs. Time)
#
# ... using Pandas plotting.
#
#  1. ax = data.plot(x="Time",y="VortSfc", option, option...
#        ... with options:
#              color='r'          ... for solid red VortSfc
#              figsize=(10,6)     ... set figsize inside the .plot()
#
#  2. data.plot(x="Time",y="P", option, option...
#        ... with options:
#              color='b'          ... for blue
#              style='--'         ... for Dashed blue
#              legend=True        ... to add a legend
#              secondary_y=True   ... to use the right-Y axis for plot
#              ax=ax              ... to overlay on the prior ax=data.plot()
#
#  3. add Left Y-axis label with ax.set_ylabel() to say: VortSfc
#  4. add Right Y-axis label with, no kidding: ax.right_ax.set_ylabel('Pres');
#
#  5. grab pearson correlation coefficient code from before; use it here
#     to get r,p = sp.stats etc etc. for data.VortSfc and data.P
#
#  6. add a title that includes the r,p values, each with 2 digits after the
#     decimal point, so title looks like:
#
#          Surface vorticity and pressure vs. time, corr=X.XX, p=Y.YY'
#
#     with values of r and p in place of X.XX and Y.YY shown here.
#     ... this all goes into: ax.set_title()
#
# CHECK: you should get one solid red line (VortSfc), one dashed blue line (P),
#     a legend in the plot box, a title above the plot box, and your title should
#     show the correlation value which is approximately -0.9
#     (negatively correlated)
ax = data.plot(x="Time",y="VortSfc", color='r', figsize=(10,6))
data.plot(x="Time",y="P", color='b', style='--', legend=True, secondary_y=True, ax=ax)
ax.set_ylabel('VortSfc')
ax.right_ax.set_ylabel('Pres')

r, p = sp.stats.pearsonr(data.VortSfc, data.Time)
plt.title('Surface vorticity and pressure vs. time, corr=%.2f, p=%.2f' % (r, p))

Text(0.5, 1.0, 'Surface vorticity and pressure vs. time, corr=-0.12, p=0.41')

# >> L. SCATTER PLOT
#
#  The previous cell make clear that VortSfc and Pres increase/decrease in opposite ways,
#  hence the negative correlation.  Let's make a scatter plot showing how this happens.
#
#  1. plotly.express is already imported as 'px' at top of this notebook.
#     do you remember how to make a scatter plot with px.scatter()?
#     check your earthquake program ...
#
#  2. Make a px.scatter plot ... using fig=px.scatter( data_set, x=....)
#       data set is: data
#       x='VortSfc'
#       y='P'
#       color is data.Wlow
#       size is data.Rain
#
#  3. Add title with fig.update_layout(title_text=' ')
#       with title: Scatter plot of VortSfc vs. P
#
#  4. Your x- and y-labels are done for you when you used x='VortSfc' etc.
#  5. The colorbar is done for you also ... darker is stronger negative Wlow
#  6. Remember you can mouse-over the circles to see the data.
#
# CHECK: higher VortSfc is found only with lower (negative) values of P,
#   and strongly negative Wlow only happens with high VortSfc, low P
fig = px.scatter(
    data, 
    x='VortSfc', 
    y='P', 
    color='Wlow', 
    size='Rain',
    title='Scatter plot of VortSfc vs. P'
)

fig.update_layout(title_text='Scatter plot of VortSfc vs. P')

# >> M. CORRELATIONS
#
# Suppose we want to compare each data column to every other column and compute
# the correlation for each pair ... we can do this in one statement!
#
#  1. corr=data.corr(method='pearson')        # does everything for us!
#  2. corr                                    # shows contents of 'corr'
#
# CHECK: every field correlated against itself has correlation = 1.00, so there is
# a diagonal set of 1.000 values in the table.  Qgr is all zeros, and here: NaN
corr = data.corr(method='pearson')
corr

# >> N. HEATMAP
#
#  Let's see all those correlations in a heatmap colored-table of array 'corr'
#
#  1. Import seaborn as sb
#  2. Make a large-r figure; I used plt.figure() for a 14x8" figure
#  3. Try: sb.heatmap(corr, annot=True)
#
#  4. It isn't so easy to see what we want here.  Add this option
#     to the sb.heatmap call:  cmap='RdBu_r'
#     ... now the bold colors are for strong (+/-) correlations.
#     Find similar color maps by searching: matplotlib diverging maps

import seaborn as sb

plt.figure(figsize=(14, 8))
sb.heatmap(corr, annot=True, cmap='RdBu_r')

<Axes: >

# >> O. PLOT "IMPORTANT" FIELDS
#
# Suppose you had 1000's of fields.  You only want to see those with strong
# correlations to VortSfc.  We'll step through all fields and only plot
# those with correlation < -0.5 =or= > +0.5 .
#
#  1. Loop variable 'col' from 1 to the number of columns (2nd dimension of data)
#       (so, range() goes to columns-1 as usual)
#
#  2. Inside the loop:
#   a) print the column number (2-digit format), and the
#      name of the column (print with format %s, and use data.columns[col]
#
#   b) set 'array' to the data array for this column.  You can do that using
#      data.iloc[:,col], storing all rows and just this column to 'array'
#
#   c) set variable 'name' to the name of this column, which you can
#      get using data.columns[col]
#
#   d) we are going to omit two columns from our search: VortSfc (not need
#      to correlate VortSfc with itself), and also Qgr (which is all zeros).
#      Do this by an if statement, making sure name does not equal 'VortSfc'
#      and name does not equal 'Qgr'.  What follows are for all those fields
#      without those names:
#
#   e) Inside the if ... :  ... statement:
#
#      (1) compute the correlation r and p-value between data.VortSfc, and array
#      (2) if r is less than -0.5 or r is greater than +0.5:
#
#        *) Print: VortSfc correlated with column (insert 2-digit col),
#             name (insert name, %s), r=(insert value of r, formatted ##.##)
#        *) Repeat the cell H code for a plot of VortSfc vs. time, overlaid
#             with a plot of 'array' vs. time formatted as we did P in cell H.
#        *) Format the title as we did in cell H, inserting the column name, r and p.

for col in range(1, data.shape[1]):
    print(f"{col:02d}  {data.columns[col]}")

    array = data.iloc[:, col]
    name = data.columns[col]

    if name != 'VortSfc' and name != 'Qgr':
        r, p = sp.stats.pearsonr(data['VortSfc'], array)
        if r < -0.5 or r > 0.5:
            print(f"VortSfc correlated with column {col:02d}, {name}: r={r:.2f}")

            plt.figure(figsize=(8, 4))
            plt.plot(data['Time'], data['VortSfc'], 'r', label='VortSfc')
            plt.plot(data['Time'], array, 'b', label=name)
            plt.xlabel('Time (min)')
            plt.ylabel('Value')
            plt.title(f'Correlation of VortSfc with {name}: r={r:.2f}, p={p:.2f}')
            plt.legend()
            plt.grid()
            plt.show()

01  dBZ2k
02  dBZmx
03  RHsfc
04  Rain
VortSfc correlated with column 04, Rain: r=0.53

05  P
VortSfc correlated with column 05, P: r=-0.92

06  VortSfc
07  VortAll
VortSfc correlated with column 07, VortAll: r=0.98

08  VrtDepth
09  Usfc
10  Vsfc
11  Wlow
12  Wmin
13  Wmax
14  Tsfc
15  TPsfc
16  Tgrad
17  Qgr
18  Qra
19  Convg

# USE THIS cell to SAVE NOTEBOOK as HTML
# %%shell
# jupyter nbconvert --to html  NAME

	Time	dBZ2k	dBZmx	RHsfc	Rain	P	VortSfc	VortAll	VrtDepth	Usfc	Vsfc	Wlow	Wmin	Wmax	Tsfc	TPsfc	Tgrad	Qgr	Qra	Convg
count	48.00	48.00000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.000000	48.0	48.000000	48.000000
mean	156.50	30.77625	57.425625	72.449167	7.843750	1.121042	4696.606458	5114.847708	5889.543750	3.526250	-17.047083	0.326188	-10.351896	40.976625	18.416458	-5.400146	2.046458	0.0	1.699542	-51.996667
std	14.00	29.80198	1.864843	10.211637	7.538937	3.080681	1745.959863	1561.212046	3123.353827	4.989002	8.122507	0.478982	3.741660	13.172087	1.542732	1.542779	1.742618	0.0	2.091811	75.276802
min	133.00	-28.88000	53.060000	60.470000	0.080000	-7.930000	1802.230000	2671.210000	388.530000	-6.850000	-30.510000	-1.142000	-15.802000	12.909000	15.916000	-7.901000	0.224000	0.0	0.003000	-251.850000
25%	144.75	0.29750	56.362500	65.717500	1.280000	-0.672500	3401.330000	3798.157500	3650.387500	0.120000	-22.317500	0.048000	-13.516750	30.971500	17.318000	-6.499000	0.658250	0.0	0.165000	-101.710000
50%	156.50	46.34500	57.675000	67.505000	5.325000	2.040000	4435.430000	5038.645000	4833.870000	3.715000	-19.000000	0.290500	-10.892000	42.664500	18.563500	-5.253000	1.494500	0.0	0.581500	-37.195000
75%	168.25	54.83000	58.805000	76.130000	15.650000	3.575000	5691.807500	5927.522500	8696.152500	7.322500	-11.720000	0.657750	-7.047750	51.755250	19.143250	-4.672750	3.655250	0.0	2.357000	-1.702500
max	180.00	57.83000	61.110000	97.040000	24.320000	4.600000	8928.900000	8928.900000	11671.000000	13.580000	4.270000	1.806000	-3.354000	64.139000	22.679000	-1.137000	6.301000	0.0	6.829000	69.530000

	Time	dBZ2k	dBZmx	RHsfc	Rain	P	VortSfc	VortAll	VrtDepth	Usfc	Vsfc	Wlow	Wmin	Wmax	Tsfc	TPsfc	Tgrad	Qgr	Qra	Convg
Time	1.000000	0.451281	0.352080	0.741100	0.634987	-0.084350	-0.120668	-0.073790	-0.529740	-0.071443	-0.175972	-0.168786	0.035344	-0.306748	-0.375564	-0.375559	-0.345836	NaN	0.687666	0.325189
dBZ2k	0.451281	1.000000	0.242430	0.448200	0.667923	-0.467171	0.457351	0.523783	-0.675269	0.295435	-0.639515	0.015905	-0.074809	-0.419317	-0.385418	-0.385382	-0.742512	NaN	0.566922	-0.024436
dBZmx	0.352080	0.242430	1.000000	0.394267	0.176171	0.054086	-0.040579	-0.042227	-0.191746	0.115866	0.090010	0.033224	0.026779	-0.133033	-0.132363	-0.132416	-0.202783	NaN	0.416904	0.263101
RHsfc	0.741100	0.448200	0.394267	1.000000	0.627025	0.005712	-0.110359	-0.046650	-0.485517	-0.116116	-0.205282	-0.203442	-0.217186	-0.524591	-0.692486	-0.692474	-0.349862	NaN	0.868148	0.224168
Rain	0.634987	0.667923	0.176171	0.627025	1.000000	-0.646093	0.527057	0.570219	-0.520728	0.216468	-0.516741	-0.069115	-0.181690	-0.724653	-0.361633	-0.361605	-0.534197	NaN	0.560783	-0.079734
P	-0.084350	-0.467171	0.054086	0.005712	-0.646093	1.000000	-0.920557	-0.927561	0.197679	-0.313055	0.329824	0.065926	0.171506	0.486820	-0.078554	-0.078581	0.324154	NaN	0.114887	0.291719
VortSfc	-0.120668	0.457351	-0.040579	-0.110359	0.527057	-0.920557	1.000000	0.979268	-0.197807	0.415678	-0.404227	0.054245	-0.202023	-0.461102	0.056372	0.056402	-0.312956	NaN	-0.165940	-0.391506
VortAll	-0.073790	0.523783	-0.042227	-0.046650	0.570219	-0.927561	0.979268	1.000000	-0.253300	0.383999	-0.415142	0.058517	-0.208763	-0.481714	0.027434	0.027470	-0.352784	NaN	-0.093905	-0.389954
VrtDepth	-0.529740	-0.675269	-0.191746	-0.485517	-0.520728	0.197679	-0.197807	-0.253300	1.000000	-0.147366	0.480236	-0.035451	0.177427	0.383294	0.407452	0.407403	0.422950	NaN	-0.518279	-0.165719
Usfc	-0.071443	0.295435	0.115866	-0.116116	0.216468	-0.313055	0.415678	0.383999	-0.147366	1.000000	-0.544603	-0.182324	0.008598	-0.103661	-0.267696	-0.267757	-0.497653	NaN	0.090374	0.274228
Vsfc	-0.175972	-0.639515	0.090010	-0.205282	-0.516741	0.329824	-0.404227	-0.415142	0.480236	-0.544603	1.000000	-0.199312	-0.012037	0.289031	0.381632	0.381595	0.579262	NaN	-0.268843	0.150925
Wlow	-0.168786	0.015905	0.033224	-0.203442	-0.069115	0.065926	0.054245	0.058517	-0.035451	-0.182324	-0.199312	1.000000	0.386809	0.031383	0.439849	0.439892	0.246464	NaN	-0.229421	-0.680603
Wmin	0.035344	-0.074809	0.026779	-0.217186	-0.181690	0.171506	-0.202023	-0.208763	0.177427	0.008598	-0.012037	0.386809	1.000000	0.357567	0.314800	0.314821	0.099422	NaN	-0.194558	-0.262679
Wmax	-0.306748	-0.419317	-0.133033	-0.524591	-0.724653	0.486820	-0.461102	-0.481714	0.383294	-0.103661	0.289031	0.031383	0.357567	1.000000	0.331543	0.331542	0.248018	NaN	-0.443343	0.110506
Tsfc	-0.375564	-0.385418	-0.132363	-0.692486	-0.361633	-0.078554	0.056372	0.027434	0.407452	-0.267696	0.381632	0.439849	0.314800	0.331543	1.000000	1.000000	0.506058	NaN	-0.687064	-0.428210
TPsfc	-0.375559	-0.385382	-0.132416	-0.692474	-0.361605	-0.078581	0.056402	0.027470	0.407403	-0.267757	0.381595	0.439892	0.314821	0.331542	1.000000	1.000000	0.506061	NaN	-0.687081	-0.428301
Tgrad	-0.345836	-0.742512	-0.202783	-0.349862	-0.534197	0.324154	-0.312956	-0.352784	0.422950	-0.497653	0.579262	0.246464	0.099422	0.248018	0.506058	0.506061	1.000000	NaN	-0.546954	-0.212137
Qgr	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Qra	0.687666	0.566922	0.416904	0.868148	0.560783	0.114887	-0.165940	-0.093905	-0.518279	0.090374	-0.268843	-0.229421	-0.194558	-0.443343	-0.687064	-0.687081	-0.546954	NaN	1.000000	0.388831
Convg	0.325189	-0.024436	0.263101	0.224168	-0.079734	0.291719	-0.391506	-0.389954	-0.165719	0.274228	0.150925	-0.680603	-0.262679	0.110506	-0.428210	-0.428301	-0.212137	NaN	0.388831	1.000000

	Time	dBZ2k	dBZmx	RHsfc	Rain	P	VortSfc	VortAll	VrtDepth	Usfc	Vsfc	Wlow	Wmin	Wmax	Tsfc	TPsfc	Tgrad	Qra	Convg
0	133.0	-28.88	56.42	72.46	0.55	3.98	2339.78	3234.00	7740.93	-1.27	-3.00	0.503	-9.556	42.377	18.735	-5.082	6.301	0.099	-44.75
1	134.0	-0.85	59.45	67.94	2.70	3.54	3297.29	3818.93	9630.71	4.57	-20.40	0.737	-14.435	36.518	19.294	-4.523	2.399	0.061	-66.85
2	135.0	2.69	56.53	70.85	1.34	3.69	4485.29	4776.70	6065.68	-1.75	-15.07	0.656	-10.649	35.898	18.108	-5.708	3.764	0.291	-180.13
3	136.0	27.36	56.38	65.93	2.03	4.04	5078.42	5078.42	8141.88	4.84	-19.45	0.874	-14.098	39.383	17.715	-6.102	4.081	0.406	-150.51
4	137.0	0.39	56.47	63.59	1.57	3.08	4797.01	5002.22	11135.74	9.71	-23.83	0.248	-13.585	35.762	18.301	-5.516	2.960	0.234	-41.54

CORRELATION¶